Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [69,6,Mod(1,69)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(69, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("69.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 69 = 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 69.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(11.0664835671\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{29}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 7 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.19258\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 69.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 10.7703 | 1.90394 | 0.951972 | − | 0.306186i | \(-0.0990530\pi\) | ||||
0.951972 | + | 0.306186i | \(0.0990530\pi\) | |||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | 84.0000 | 2.62500 | ||||||||
\(5\) | 52.3852 | 0.937094 | 0.468547 | − | 0.883438i | \(-0.344778\pi\) | ||||
0.468547 | + | 0.883438i | \(0.344778\pi\) | |||||||
\(6\) | −96.9330 | −1.09924 | ||||||||
\(7\) | −118.237 | −0.912027 | −0.456013 | − | 0.889973i | \(-0.650723\pi\) | ||||
−0.456013 | + | 0.889973i | \(0.650723\pi\) | |||||||
\(8\) | 560.057 | 3.09391 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 564.205 | 1.78417 | ||||||||
\(11\) | 741.598 | 1.84794 | 0.923968 | − | 0.382471i | \(-0.124927\pi\) | ||||
0.923968 | + | 0.382471i | \(0.124927\pi\) | |||||||
\(12\) | −756.000 | −1.51554 | ||||||||
\(13\) | −542.502 | −0.890314 | −0.445157 | − | 0.895453i | \(-0.646852\pi\) | ||||
−0.445157 | + | 0.895453i | \(0.646852\pi\) | |||||||
\(14\) | −1273.45 | −1.73645 | ||||||||
\(15\) | −471.466 | −0.541032 | ||||||||
\(16\) | 3344.00 | 3.26562 | ||||||||
\(17\) | −834.993 | −0.700746 | −0.350373 | − | 0.936610i | \(-0.613945\pi\) | ||||
−0.350373 | + | 0.936610i | \(0.613945\pi\) | |||||||
\(18\) | 872.397 | 0.634648 | ||||||||
\(19\) | −1309.79 | −0.832370 | −0.416185 | − | 0.909280i | \(-0.636633\pi\) | ||||
−0.416185 | + | 0.909280i | \(0.636633\pi\) | |||||||
\(20\) | 4400.35 | 2.45987 | ||||||||
\(21\) | 1064.13 | 0.526559 | ||||||||
\(22\) | 7987.25 | 3.51836 | ||||||||
\(23\) | 529.000 | 0.208514 | ||||||||
\(24\) | −5040.51 | −1.78627 | ||||||||
\(25\) | −380.795 | −0.121854 | ||||||||
\(26\) | −5842.93 | −1.69511 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | −9931.89 | −2.39407 | ||||||||
\(29\) | 5536.45 | 1.22247 | 0.611233 | − | 0.791451i | \(-0.290674\pi\) | ||||
0.611233 | + | 0.791451i | \(0.290674\pi\) | |||||||
\(30\) | −5077.85 | −1.03009 | ||||||||
\(31\) | −7267.14 | −1.35819 | −0.679093 | − | 0.734052i | \(-0.737627\pi\) | ||||
−0.679093 | + | 0.734052i | \(0.737627\pi\) | |||||||
\(32\) | 18094.2 | 3.12366 | ||||||||
\(33\) | −6674.38 | −1.06691 | ||||||||
\(34\) | −8993.15 | −1.33418 | ||||||||
\(35\) | −6193.85 | −0.854655 | ||||||||
\(36\) | 6804.00 | 0.875000 | ||||||||
\(37\) | −10446.7 | −1.25451 | −0.627253 | − | 0.778815i | \(-0.715821\pi\) | ||||
−0.627253 | + | 0.778815i | \(0.715821\pi\) | |||||||
\(38\) | −14106.8 | −1.58479 | ||||||||
\(39\) | 4882.52 | 0.514023 | ||||||||
\(40\) | 29338.7 | 2.89928 | ||||||||
\(41\) | −4630.45 | −0.430193 | −0.215096 | − | 0.976593i | \(-0.569007\pi\) | ||||
−0.215096 | + | 0.976593i | \(0.569007\pi\) | |||||||
\(42\) | 11461.0 | 1.00254 | ||||||||
\(43\) | −9201.23 | −0.758883 | −0.379442 | − | 0.925216i | \(-0.623884\pi\) | ||||
−0.379442 | + | 0.925216i | \(0.623884\pi\) | |||||||
\(44\) | 62294.2 | 4.85083 | ||||||||
\(45\) | 4243.20 | 0.312365 | ||||||||
\(46\) | 5697.50 | 0.397000 | ||||||||
\(47\) | 15272.3 | 1.00846 | 0.504231 | − | 0.863569i | \(-0.331776\pi\) | ||||
0.504231 | + | 0.863569i | \(0.331776\pi\) | |||||||
\(48\) | −30096.0 | −1.88541 | ||||||||
\(49\) | −2827.06 | −0.168207 | ||||||||
\(50\) | −4101.28 | −0.232004 | ||||||||
\(51\) | 7514.94 | 0.404576 | ||||||||
\(52\) | −45570.2 | −2.33707 | ||||||||
\(53\) | −36202.8 | −1.77032 | −0.885161 | − | 0.465285i | \(-0.845952\pi\) | ||||
−0.885161 | + | 0.465285i | \(0.845952\pi\) | |||||||
\(54\) | −7851.57 | −0.366414 | ||||||||
\(55\) | 38848.7 | 1.73169 | ||||||||
\(56\) | −66219.4 | −2.82173 | ||||||||
\(57\) | 11788.1 | 0.480569 | ||||||||
\(58\) | 59629.4 | 2.32751 | ||||||||
\(59\) | 6436.34 | 0.240718 | 0.120359 | − | 0.992730i | \(-0.461595\pi\) | ||||
0.120359 | + | 0.992730i | \(0.461595\pi\) | |||||||
\(60\) | −39603.2 | −1.42021 | ||||||||
\(61\) | −2637.86 | −0.0907668 | −0.0453834 | − | 0.998970i | \(-0.514451\pi\) | ||||
−0.0453834 | + | 0.998970i | \(0.514451\pi\) | |||||||
\(62\) | −78269.5 | −2.58591 | ||||||||
\(63\) | −9577.18 | −0.304009 | ||||||||
\(64\) | 87872.0 | 2.68164 | ||||||||
\(65\) | −28419.1 | −0.834308 | ||||||||
\(66\) | −71885.3 | −2.03133 | ||||||||
\(67\) | 21068.5 | 0.573384 | 0.286692 | − | 0.958023i | \(-0.407444\pi\) | ||||
0.286692 | + | 0.958023i | \(0.407444\pi\) | |||||||
\(68\) | −70139.4 | −1.83946 | ||||||||
\(69\) | −4761.00 | −0.120386 | ||||||||
\(70\) | −66709.9 | −1.62721 | ||||||||
\(71\) | 74668.2 | 1.75788 | 0.878941 | − | 0.476930i | \(-0.158250\pi\) | ||||
0.878941 | + | 0.476930i | \(0.158250\pi\) | |||||||
\(72\) | 45364.6 | 1.03130 | ||||||||
\(73\) | 80742.0 | 1.77334 | 0.886671 | − | 0.462402i | \(-0.153012\pi\) | ||||
0.886671 | + | 0.462402i | \(0.153012\pi\) | |||||||
\(74\) | −112514. | −2.38851 | ||||||||
\(75\) | 3427.15 | 0.0703526 | ||||||||
\(76\) | −110022. | −2.18497 | ||||||||
\(77\) | −87684.2 | −1.68537 | ||||||||
\(78\) | 52586.3 | 0.978671 | ||||||||
\(79\) | 39107.7 | 0.705008 | 0.352504 | − | 0.935810i | \(-0.385330\pi\) | ||||
0.352504 | + | 0.935810i | \(0.385330\pi\) | |||||||
\(80\) | 175176. | 3.06020 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −49871.4 | −0.819063 | ||||||||
\(83\) | 101465. | 1.61666 | 0.808331 | − | 0.588728i | \(-0.200371\pi\) | ||||
0.808331 | + | 0.588728i | \(0.200371\pi\) | |||||||
\(84\) | 89387.0 | 1.38222 | ||||||||
\(85\) | −43741.2 | −0.656665 | ||||||||
\(86\) | −99100.3 | −1.44487 | ||||||||
\(87\) | −49828.1 | −0.705791 | ||||||||
\(88\) | 415337. | 5.71734 | ||||||||
\(89\) | 22407.6 | 0.299861 | 0.149930 | − | 0.988697i | \(-0.452095\pi\) | ||||
0.149930 | + | 0.988697i | \(0.452095\pi\) | |||||||
\(90\) | 45700.6 | 0.594725 | ||||||||
\(91\) | 64143.7 | 0.811990 | ||||||||
\(92\) | 44436.0 | 0.547350 | ||||||||
\(93\) | 65404.3 | 0.784149 | ||||||||
\(94\) | 164488. | 1.92005 | ||||||||
\(95\) | −68613.4 | −0.780009 | ||||||||
\(96\) | −162847. | −1.80344 | ||||||||
\(97\) | −29724.8 | −0.320767 | −0.160384 | − | 0.987055i | \(-0.551273\pi\) | ||||
−0.160384 | + | 0.987055i | \(0.551273\pi\) | |||||||
\(98\) | −30448.3 | −0.320257 | ||||||||
\(99\) | 60069.4 | 0.615978 | ||||||||
\(100\) | −31986.7 | −0.319867 | ||||||||
\(101\) | 96859.7 | 0.944800 | 0.472400 | − | 0.881384i | \(-0.343388\pi\) | ||||
0.472400 | + | 0.881384i | \(0.343388\pi\) | |||||||
\(102\) | 80938.3 | 0.770289 | ||||||||
\(103\) | 2081.11 | 0.0193287 | 0.00966434 | − | 0.999953i | \(-0.496924\pi\) | ||||
0.00966434 | + | 0.999953i | \(0.496924\pi\) | |||||||
\(104\) | −303832. | −2.75455 | ||||||||
\(105\) | 55744.7 | 0.493435 | ||||||||
\(106\) | −389916. | −3.37059 | ||||||||
\(107\) | −76907.3 | −0.649393 | −0.324697 | − | 0.945818i | \(-0.605262\pi\) | ||||
−0.324697 | + | 0.945818i | \(0.605262\pi\) | |||||||
\(108\) | −61236.0 | −0.505181 | ||||||||
\(109\) | −27250.0 | −0.219685 | −0.109842 | − | 0.993949i | \(-0.535035\pi\) | ||||
−0.109842 | + | 0.993949i | \(0.535035\pi\) | |||||||
\(110\) | 418414. | 3.29704 | ||||||||
\(111\) | 94019.9 | 0.724290 | ||||||||
\(112\) | −395384. | −2.97834 | ||||||||
\(113\) | −120738. | −0.889505 | −0.444753 | − | 0.895653i | \(-0.646708\pi\) | ||||
−0.444753 | + | 0.895653i | \(0.646708\pi\) | |||||||
\(114\) | 126961. | 0.914976 | ||||||||
\(115\) | 27711.8 | 0.195398 | ||||||||
\(116\) | 465062. | 3.20897 | ||||||||
\(117\) | −43942.7 | −0.296771 | ||||||||
\(118\) | 69321.5 | 0.458314 | ||||||||
\(119\) | 98726.9 | 0.639099 | ||||||||
\(120\) | −264048. | −1.67390 | ||||||||
\(121\) | 388916. | 2.41486 | ||||||||
\(122\) | −28410.6 | −0.172815 | ||||||||
\(123\) | 41674.0 | 0.248372 | ||||||||
\(124\) | −610440. | −3.56524 | ||||||||
\(125\) | −183652. | −1.05128 | ||||||||
\(126\) | −103149. | −0.578816 | ||||||||
\(127\) | −140823. | −0.774755 | −0.387377 | − | 0.921921i | \(-0.626619\pi\) | ||||
−0.387377 | + | 0.921921i | \(0.626619\pi\) | |||||||
\(128\) | 367397. | 1.98203 | ||||||||
\(129\) | 82811.1 | 0.438141 | ||||||||
\(130\) | −306083. | −1.58848 | ||||||||
\(131\) | −137026. | −0.697630 | −0.348815 | − | 0.937192i | \(-0.613416\pi\) | ||||
−0.348815 | + | 0.937192i | \(0.613416\pi\) | |||||||
\(132\) | −560648. | −2.80063 | ||||||||
\(133\) | 154865. | 0.759144 | ||||||||
\(134\) | 226914. | 1.09169 | ||||||||
\(135\) | −38188.8 | −0.180344 | ||||||||
\(136\) | −467644. | −2.16804 | ||||||||
\(137\) | 73627.5 | 0.335149 | 0.167575 | − | 0.985859i | \(-0.446406\pi\) | ||||
0.167575 | + | 0.985859i | \(0.446406\pi\) | |||||||
\(138\) | −51277.5 | −0.229208 | ||||||||
\(139\) | 214252. | 0.940562 | 0.470281 | − | 0.882517i | \(-0.344152\pi\) | ||||
0.470281 | + | 0.882517i | \(0.344152\pi\) | |||||||
\(140\) | −520284. | −2.24347 | ||||||||
\(141\) | −137451. | −0.582236 | ||||||||
\(142\) | 804201. | 3.34691 | ||||||||
\(143\) | −402318. | −1.64524 | ||||||||
\(144\) | 270864. | 1.08854 | ||||||||
\(145\) | 290028. | 1.14557 | ||||||||
\(146\) | 869618. | 3.37634 | ||||||||
\(147\) | 25443.5 | 0.0971144 | ||||||||
\(148\) | −877519. | −3.29308 | ||||||||
\(149\) | 132470. | 0.488823 | 0.244412 | − | 0.969672i | \(-0.421405\pi\) | ||||
0.244412 | + | 0.969672i | \(0.421405\pi\) | |||||||
\(150\) | 36911.5 | 0.133947 | ||||||||
\(151\) | 171660. | 0.612669 | 0.306334 | − | 0.951924i | \(-0.400897\pi\) | ||||
0.306334 | + | 0.951924i | \(0.400897\pi\) | |||||||
\(152\) | −733555. | −2.57528 | ||||||||
\(153\) | −67634.4 | −0.233582 | ||||||||
\(154\) | −944387. | −3.20884 | ||||||||
\(155\) | −380690. | −1.27275 | ||||||||
\(156\) | 410132. | 1.34931 | ||||||||
\(157\) | −359852. | −1.16513 | −0.582565 | − | 0.812784i | \(-0.697951\pi\) | ||||
−0.582565 | + | 0.812784i | \(0.697951\pi\) | |||||||
\(158\) | 421202. | 1.34230 | ||||||||
\(159\) | 325825. | 1.02210 | ||||||||
\(160\) | 947865. | 2.92716 | ||||||||
\(161\) | −62547.3 | −0.190171 | ||||||||
\(162\) | 70664.1 | 0.211549 | ||||||||
\(163\) | 454656. | 1.34034 | 0.670168 | − | 0.742210i | \(-0.266222\pi\) | ||||
0.670168 | + | 0.742210i | \(0.266222\pi\) | |||||||
\(164\) | −388957. | −1.12926 | ||||||||
\(165\) | −349639. | −0.999791 | ||||||||
\(166\) | 1.09281e6 | 3.07803 | ||||||||
\(167\) | −359837. | −0.998424 | −0.499212 | − | 0.866480i | \(-0.666377\pi\) | ||||
−0.499212 | + | 0.866480i | \(0.666377\pi\) | |||||||
\(168\) | 595974. | 1.62912 | ||||||||
\(169\) | −76984.4 | −0.207341 | ||||||||
\(170\) | −471108. | −1.25025 | ||||||||
\(171\) | −106093. | −0.277457 | ||||||||
\(172\) | −772904. | −1.99207 | ||||||||
\(173\) | −308025. | −0.782476 | −0.391238 | − | 0.920289i | \(-0.627953\pi\) | ||||
−0.391238 | + | 0.920289i | \(0.627953\pi\) | |||||||
\(174\) | −536665. | −1.34379 | ||||||||
\(175\) | 45023.9 | 0.111134 | ||||||||
\(176\) | 2.47990e6 | 6.03466 | ||||||||
\(177\) | −57927.0 | −0.138979 | ||||||||
\(178\) | 241337. | 0.570918 | ||||||||
\(179\) | 628893. | 1.46705 | 0.733524 | − | 0.679663i | \(-0.237874\pi\) | ||||
0.733524 | + | 0.679663i | \(0.237874\pi\) | |||||||
\(180\) | 356429. | 0.819958 | ||||||||
\(181\) | −667015. | −1.51335 | −0.756675 | − | 0.653791i | \(-0.773177\pi\) | ||||
−0.756675 | + | 0.653791i | \(0.773177\pi\) | |||||||
\(182\) | 690849. | 1.54598 | ||||||||
\(183\) | 23740.7 | 0.0524043 | ||||||||
\(184\) | 296270. | 0.645124 | ||||||||
\(185\) | −547250. | −1.17559 | ||||||||
\(186\) | 704425. | 1.49298 | ||||||||
\(187\) | −619229. | −1.29493 | ||||||||
\(188\) | 1.28287e6 | 2.64721 | ||||||||
\(189\) | 86194.6 | 0.175520 | ||||||||
\(190\) | −738989. | −1.48509 | ||||||||
\(191\) | 573327. | 1.13715 | 0.568577 | − | 0.822630i | \(-0.307494\pi\) | ||||
0.568577 | + | 0.822630i | \(0.307494\pi\) | |||||||
\(192\) | −790848. | −1.54825 | ||||||||
\(193\) | 21198.3 | 0.0409646 | 0.0204823 | − | 0.999790i | \(-0.493480\pi\) | ||||
0.0204823 | + | 0.999790i | \(0.493480\pi\) | |||||||
\(194\) | −320146. | −0.610722 | ||||||||
\(195\) | 255772. | 0.481688 | ||||||||
\(196\) | −237473. | −0.441544 | ||||||||
\(197\) | −342207. | −0.628237 | −0.314118 | − | 0.949384i | \(-0.601709\pi\) | ||||
−0.314118 | + | 0.949384i | \(0.601709\pi\) | |||||||
\(198\) | 646967. | 1.17279 | ||||||||
\(199\) | −32335.5 | −0.0578825 | −0.0289412 | − | 0.999581i | \(-0.509214\pi\) | ||||
−0.0289412 | + | 0.999581i | \(0.509214\pi\) | |||||||
\(200\) | −213267. | −0.377006 | ||||||||
\(201\) | −189616. | −0.331043 | ||||||||
\(202\) | 1.04321e6 | 1.79885 | ||||||||
\(203\) | −654613. | −1.11492 | ||||||||
\(204\) | 631255. | 1.06201 | ||||||||
\(205\) | −242567. | −0.403131 | ||||||||
\(206\) | 22414.3 | 0.0368007 | ||||||||
\(207\) | 42849.0 | 0.0695048 | ||||||||
\(208\) | −1.81413e6 | −2.90743 | ||||||||
\(209\) | −971335. | −1.53817 | ||||||||
\(210\) | 600389. | 0.939473 | ||||||||
\(211\) | −1.03399e6 | −1.59886 | −0.799430 | − | 0.600759i | \(-0.794865\pi\) | ||||
−0.799430 | + | 0.600759i | \(0.794865\pi\) | |||||||
\(212\) | −3.04103e6 | −4.64710 | ||||||||
\(213\) | −672014. | −1.01491 | ||||||||
\(214\) | −828317. | −1.23641 | ||||||||
\(215\) | −482008. | −0.711145 | ||||||||
\(216\) | −408282. | −0.595423 | ||||||||
\(217\) | 859243. | 1.23870 | ||||||||
\(218\) | −293491. | −0.418267 | ||||||||
\(219\) | −726678. | −1.02384 | ||||||||
\(220\) | 3.26329e6 | 4.54568 | ||||||||
\(221\) | 452985. | 0.623884 | ||||||||
\(222\) | 1.01263e6 | 1.37901 | ||||||||
\(223\) | 990187. | 1.33338 | 0.666692 | − | 0.745333i | \(-0.267710\pi\) | ||||
0.666692 | + | 0.745333i | \(0.267710\pi\) | |||||||
\(224\) | −2.13940e6 | −2.84886 | ||||||||
\(225\) | −30844.4 | −0.0406181 | ||||||||
\(226\) | −1.30039e6 | −1.69357 | ||||||||
\(227\) | −26685.3 | −0.0343723 | −0.0171861 | − | 0.999852i | \(-0.505471\pi\) | ||||
−0.0171861 | + | 0.999852i | \(0.505471\pi\) | |||||||
\(228\) | 990198. | 1.26149 | ||||||||
\(229\) | 150586. | 0.189756 | 0.0948778 | − | 0.995489i | \(-0.469754\pi\) | ||||
0.0948778 | + | 0.995489i | \(0.469754\pi\) | |||||||
\(230\) | 298465. | 0.372026 | ||||||||
\(231\) | 789157. | 0.973047 | ||||||||
\(232\) | 3.10073e6 | 3.78220 | ||||||||
\(233\) | 1.29421e6 | 1.56176 | 0.780881 | − | 0.624680i | \(-0.214770\pi\) | ||||
0.780881 | + | 0.624680i | \(0.214770\pi\) | |||||||
\(234\) | −473277. | −0.565036 | ||||||||
\(235\) | 800041. | 0.945024 | ||||||||
\(236\) | 540652. | 0.631885 | ||||||||
\(237\) | −351969. | −0.407037 | ||||||||
\(238\) | 1.06332e6 | 1.21681 | ||||||||
\(239\) | −136898. | −0.155025 | −0.0775123 | − | 0.996991i | \(-0.524698\pi\) | ||||
−0.0775123 | + | 0.996991i | \(0.524698\pi\) | |||||||
\(240\) | −1.57658e6 | −1.76681 | ||||||||
\(241\) | −284796. | −0.315858 | −0.157929 | − | 0.987450i | \(-0.550482\pi\) | ||||
−0.157929 | + | 0.987450i | \(0.550482\pi\) | |||||||
\(242\) | 4.18876e6 | 4.59776 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | −221580. | −0.238263 | ||||||||
\(245\) | −148096. | −0.157626 | ||||||||
\(246\) | 448843. | 0.472886 | ||||||||
\(247\) | 710562. | 0.741071 | ||||||||
\(248\) | −4.07001e6 | −4.20210 | ||||||||
\(249\) | −913181. | −0.933380 | ||||||||
\(250\) | −1.97799e6 | −2.00158 | ||||||||
\(251\) | 1.26148e6 | 1.26385 | 0.631927 | − | 0.775028i | \(-0.282264\pi\) | ||||
0.631927 | + | 0.775028i | \(0.282264\pi\) | |||||||
\(252\) | −804483. | −0.798023 | ||||||||
\(253\) | 392305. | 0.385321 | ||||||||
\(254\) | −1.51671e6 | −1.47509 | ||||||||
\(255\) | 393671. | 0.379126 | ||||||||
\(256\) | 1.14509e6 | 1.09204 | ||||||||
\(257\) | 552720. | 0.522002 | 0.261001 | − | 0.965338i | \(-0.415947\pi\) | ||||
0.261001 | + | 0.965338i | \(0.415947\pi\) | |||||||
\(258\) | 891903. | 0.834196 | ||||||||
\(259\) | 1.23518e6 | 1.14414 | ||||||||
\(260\) | −2.38720e6 | −2.19006 | ||||||||
\(261\) | 448453. | 0.407489 | ||||||||
\(262\) | −1.47582e6 | −1.32825 | ||||||||
\(263\) | −651514. | −0.580811 | −0.290405 | − | 0.956904i | \(-0.593790\pi\) | ||||
−0.290405 | + | 0.956904i | \(0.593790\pi\) | |||||||
\(264\) | −3.73803e6 | −3.30091 | ||||||||
\(265\) | −1.89649e6 | −1.65896 | ||||||||
\(266\) | 1.66795e6 | 1.44537 | ||||||||
\(267\) | −201668. | −0.173125 | ||||||||
\(268\) | 1.76975e6 | 1.50513 | ||||||||
\(269\) | 1.62659e6 | 1.37056 | 0.685280 | − | 0.728280i | \(-0.259680\pi\) | ||||
0.685280 | + | 0.728280i | \(0.259680\pi\) | |||||||
\(270\) | −411306. | −0.343365 | ||||||||
\(271\) | 526548. | 0.435527 | 0.217763 | − | 0.976002i | \(-0.430124\pi\) | ||||
0.217763 | + | 0.976002i | \(0.430124\pi\) | |||||||
\(272\) | −2.79222e6 | −2.28837 | ||||||||
\(273\) | −577294. | −0.468803 | ||||||||
\(274\) | 792992. | 0.638106 | ||||||||
\(275\) | −282396. | −0.225179 | ||||||||
\(276\) | −399924. | −0.316013 | ||||||||
\(277\) | 102974. | 0.0806358 | 0.0403179 | − | 0.999187i | \(-0.487163\pi\) | ||||
0.0403179 | + | 0.999187i | \(0.487163\pi\) | |||||||
\(278\) | 2.30756e6 | 1.79078 | ||||||||
\(279\) | −588638. | −0.452729 | ||||||||
\(280\) | −3.46891e6 | −2.64422 | ||||||||
\(281\) | −1.79209e6 | −1.35392 | −0.676960 | − | 0.736020i | \(-0.736703\pi\) | ||||
−0.676960 | + | 0.736020i | \(0.736703\pi\) | |||||||
\(282\) | −1.48039e6 | −1.10854 | ||||||||
\(283\) | −1.06565e6 | −0.790946 | −0.395473 | − | 0.918478i | \(-0.629419\pi\) | ||||
−0.395473 | + | 0.918478i | \(0.629419\pi\) | |||||||
\(284\) | 6.27213e6 | 4.61444 | ||||||||
\(285\) | 617520. | 0.450339 | ||||||||
\(286\) | −4.33310e6 | −3.13245 | ||||||||
\(287\) | 547489. | 0.392347 | ||||||||
\(288\) | 1.46563e6 | 1.04122 | ||||||||
\(289\) | −722644. | −0.508955 | ||||||||
\(290\) | 3.12370e6 | 2.18109 | ||||||||
\(291\) | 267523. | 0.185195 | ||||||||
\(292\) | 6.78233e6 | 4.65502 | ||||||||
\(293\) | 1.85858e6 | 1.26477 | 0.632387 | − | 0.774653i | \(-0.282075\pi\) | ||||
0.632387 | + | 0.774653i | \(0.282075\pi\) | |||||||
\(294\) | 274035. | 0.184900 | ||||||||
\(295\) | 337169. | 0.225576 | ||||||||
\(296\) | −5.85072e6 | −3.88133 | ||||||||
\(297\) | −540625. | −0.355635 | ||||||||
\(298\) | 1.42675e6 | 0.930692 | ||||||||
\(299\) | −286984. | −0.185643 | ||||||||
\(300\) | 287881. | 0.184676 | ||||||||
\(301\) | 1.08792e6 | 0.692122 | ||||||||
\(302\) | 1.84883e6 | 1.16649 | ||||||||
\(303\) | −871738. | −0.545480 | ||||||||
\(304\) | −4.37993e6 | −2.71821 | ||||||||
\(305\) | −138185. | −0.0850571 | ||||||||
\(306\) | −728445. | −0.444727 | ||||||||
\(307\) | −2.13805e6 | −1.29471 | −0.647355 | − | 0.762189i | \(-0.724125\pi\) | ||||
−0.647355 | + | 0.762189i | \(0.724125\pi\) | |||||||
\(308\) | −7.36547e6 | −4.42409 | ||||||||
\(309\) | −18730.0 | −0.0111594 | ||||||||
\(310\) | −4.10016e6 | −2.42324 | ||||||||
\(311\) | 1.35485e6 | 0.794311 | 0.397155 | − | 0.917751i | \(-0.369997\pi\) | ||||
0.397155 | + | 0.917751i | \(0.369997\pi\) | |||||||
\(312\) | 2.73449e6 | 1.59034 | ||||||||
\(313\) | −523789. | −0.302201 | −0.151100 | − | 0.988518i | \(-0.548282\pi\) | ||||
−0.151100 | + | 0.988518i | \(0.548282\pi\) | |||||||
\(314\) | −3.87572e6 | −2.21834 | ||||||||
\(315\) | −501702. | −0.284885 | ||||||||
\(316\) | 3.28504e6 | 1.85065 | ||||||||
\(317\) | 2.59918e6 | 1.45274 | 0.726371 | − | 0.687302i | \(-0.241205\pi\) | ||||
0.726371 | + | 0.687302i | \(0.241205\pi\) | |||||||
\(318\) | 3.50924e6 | 1.94601 | ||||||||
\(319\) | 4.10582e6 | 2.25904 | ||||||||
\(320\) | 4.60319e6 | 2.51295 | ||||||||
\(321\) | 692165. | 0.374928 | ||||||||
\(322\) | −673655. | −0.362074 | ||||||||
\(323\) | 1.09366e6 | 0.583280 | ||||||||
\(324\) | 551124. | 0.291667 | ||||||||
\(325\) | 206582. | 0.108489 | ||||||||
\(326\) | 4.89679e6 | 2.55192 | ||||||||
\(327\) | 245250. | 0.126835 | ||||||||
\(328\) | −2.59331e6 | −1.33098 | ||||||||
\(329\) | −1.80575e6 | −0.919744 | ||||||||
\(330\) | −3.76572e6 | −1.90355 | ||||||||
\(331\) | −1.02887e6 | −0.516168 | −0.258084 | − | 0.966122i | \(-0.583091\pi\) | ||||
−0.258084 | + | 0.966122i | \(0.583091\pi\) | |||||||
\(332\) | 8.52302e6 | 4.24374 | ||||||||
\(333\) | −846179. | −0.418169 | ||||||||
\(334\) | −3.87557e6 | −1.90094 | ||||||||
\(335\) | 1.10367e6 | 0.537315 | ||||||||
\(336\) | 3.55846e6 | 1.71954 | ||||||||
\(337\) | 1.13501e6 | 0.544406 | 0.272203 | − | 0.962240i | \(-0.412248\pi\) | ||||
0.272203 | + | 0.962240i | \(0.412248\pi\) | |||||||
\(338\) | −829147. | −0.394766 | ||||||||
\(339\) | 1.08664e6 | 0.513556 | ||||||||
\(340\) | −3.67426e6 | −1.72375 | ||||||||
\(341\) | −5.38929e6 | −2.50984 | ||||||||
\(342\) | −1.14265e6 | −0.528262 | ||||||||
\(343\) | 2.32147e6 | 1.06544 | ||||||||
\(344\) | −5.15322e6 | −2.34791 | ||||||||
\(345\) | −249406. | −0.112813 | ||||||||
\(346\) | −3.31753e6 | −1.48979 | ||||||||
\(347\) | 1.08736e6 | 0.484787 | 0.242393 | − | 0.970178i | \(-0.422068\pi\) | ||||
0.242393 | + | 0.970178i | \(0.422068\pi\) | |||||||
\(348\) | −4.18556e6 | −1.85270 | ||||||||
\(349\) | 147242. | 0.0647097 | 0.0323548 | − | 0.999476i | \(-0.489699\pi\) | ||||
0.0323548 | + | 0.999476i | \(0.489699\pi\) | |||||||
\(350\) | 484923. | 0.211593 | ||||||||
\(351\) | 395484. | 0.171341 | ||||||||
\(352\) | 1.34186e7 | 5.77232 | ||||||||
\(353\) | 1.58645e6 | 0.677623 | 0.338812 | − | 0.940854i | \(-0.389975\pi\) | ||||
0.338812 | + | 0.940854i | \(0.389975\pi\) | |||||||
\(354\) | −623893. | −0.264607 | ||||||||
\(355\) | 3.91151e6 | 1.64730 | ||||||||
\(356\) | 1.88224e6 | 0.787135 | ||||||||
\(357\) | −888542. | −0.368984 | ||||||||
\(358\) | 6.77339e6 | 2.79318 | ||||||||
\(359\) | −1.85640e6 | −0.760211 | −0.380106 | − | 0.924943i | \(-0.624112\pi\) | ||||
−0.380106 | + | 0.924943i | \(0.624112\pi\) | |||||||
\(360\) | 2.37643e6 | 0.966428 | ||||||||
\(361\) | −760559. | −0.307160 | ||||||||
\(362\) | −7.18397e6 | −2.88133 | ||||||||
\(363\) | −3.50025e6 | −1.39422 | ||||||||
\(364\) | 5.38807e6 | 2.13147 | ||||||||
\(365\) | 4.22968e6 | 1.66179 | ||||||||
\(366\) | 255696. | 0.0997747 | ||||||||
\(367\) | −2.01535e6 | −0.781061 | −0.390531 | − | 0.920590i | \(-0.627708\pi\) | ||||
−0.390531 | + | 0.920590i | \(0.627708\pi\) | |||||||
\(368\) | 1.76898e6 | 0.680930 | ||||||||
\(369\) | −375066. | −0.143398 | ||||||||
\(370\) | −5.89406e6 | −2.23826 | ||||||||
\(371\) | 4.28050e6 | 1.61458 | ||||||||
\(372\) | 5.49396e6 | 2.05839 | ||||||||
\(373\) | −1.33526e6 | −0.496928 | −0.248464 | − | 0.968641i | \(-0.579926\pi\) | ||||
−0.248464 | + | 0.968641i | \(0.579926\pi\) | |||||||
\(374\) | −6.66930e6 | −2.46548 | ||||||||
\(375\) | 1.65286e6 | 0.606959 | ||||||||
\(376\) | 8.55336e6 | 3.12009 | ||||||||
\(377\) | −3.00354e6 | −1.08838 | ||||||||
\(378\) | 928345. | 0.334179 | ||||||||
\(379\) | −2.84308e6 | −1.01669 | −0.508347 | − | 0.861152i | \(-0.669743\pi\) | ||||
−0.508347 | + | 0.861152i | \(0.669743\pi\) | |||||||
\(380\) | −5.76352e6 | −2.04752 | ||||||||
\(381\) | 1.26741e6 | 0.447305 | ||||||||
\(382\) | 6.17492e6 | 2.16508 | ||||||||
\(383\) | 3.29481e6 | 1.14771 | 0.573857 | − | 0.818956i | \(-0.305447\pi\) | ||||
0.573857 | + | 0.818956i | \(0.305447\pi\) | |||||||
\(384\) | −3.30658e6 | −1.14433 | ||||||||
\(385\) | −4.59335e6 | −1.57935 | ||||||||
\(386\) | 228313. | 0.0779942 | ||||||||
\(387\) | −745300. | −0.252961 | ||||||||
\(388\) | −2.49688e6 | −0.842014 | ||||||||
\(389\) | −4.92017e6 | −1.64857 | −0.824283 | − | 0.566177i | \(-0.808422\pi\) | ||||
−0.824283 | + | 0.566177i | \(0.808422\pi\) | |||||||
\(390\) | 2.75474e6 | 0.917107 | ||||||||
\(391\) | −441711. | −0.146116 | ||||||||
\(392\) | −1.58331e6 | −0.520417 | ||||||||
\(393\) | 1.23323e6 | 0.402777 | ||||||||
\(394\) | −3.68568e6 | −1.19613 | ||||||||
\(395\) | 2.04866e6 | 0.660659 | ||||||||
\(396\) | 5.04583e6 | 1.61694 | ||||||||
\(397\) | −4.13215e6 | −1.31583 | −0.657915 | − | 0.753092i | \(-0.728561\pi\) | ||||
−0.657915 | + | 0.753092i | \(0.728561\pi\) | |||||||
\(398\) | −348264. | −0.110205 | ||||||||
\(399\) | −1.39378e6 | −0.438292 | ||||||||
\(400\) | −1.27338e6 | −0.397930 | ||||||||
\(401\) | −3.07921e6 | −0.956266 | −0.478133 | − | 0.878287i | \(-0.658686\pi\) | ||||
−0.478133 | + | 0.878287i | \(0.658686\pi\) | |||||||
\(402\) | −2.04223e6 | −0.630288 | ||||||||
\(403\) | 3.94244e6 | 1.20921 | ||||||||
\(404\) | 8.13622e6 | 2.48010 | ||||||||
\(405\) | 343699. | 0.104122 | ||||||||
\(406\) | −7.05039e6 | −2.12275 | ||||||||
\(407\) | −7.74722e6 | −2.31825 | ||||||||
\(408\) | 4.20879e6 | 1.25172 | ||||||||
\(409\) | −483481. | −0.142913 | −0.0714564 | − | 0.997444i | \(-0.522765\pi\) | ||||
−0.0714564 | + | 0.997444i | \(0.522765\pi\) | |||||||
\(410\) | −2.61252e6 | −0.767539 | ||||||||
\(411\) | −662647. | −0.193499 | ||||||||
\(412\) | 174813. | 0.0507378 | ||||||||
\(413\) | −761012. | −0.219541 | ||||||||
\(414\) | 461498. | 0.132333 | ||||||||
\(415\) | 5.31524e6 | 1.51496 | ||||||||
\(416\) | −9.81612e6 | −2.78103 | ||||||||
\(417\) | −1.92827e6 | −0.543034 | ||||||||
\(418\) | −1.04616e7 | −2.92858 | ||||||||
\(419\) | 1.51752e6 | 0.422279 | 0.211140 | − | 0.977456i | \(-0.432282\pi\) | ||||
0.211140 | + | 0.977456i | \(0.432282\pi\) | |||||||
\(420\) | 4.68255e6 | 1.29527 | ||||||||
\(421\) | 3.76256e6 | 1.03461 | 0.517306 | − | 0.855800i | \(-0.326935\pi\) | ||||
0.517306 | + | 0.855800i | \(0.326935\pi\) | |||||||
\(422\) | −1.11364e7 | −3.04414 | ||||||||
\(423\) | 1.23706e6 | 0.336154 | ||||||||
\(424\) | −2.02756e7 | −5.47721 | ||||||||
\(425\) | 317961. | 0.0853888 | ||||||||
\(426\) | −7.23781e6 | −1.93234 | ||||||||
\(427\) | 311892. | 0.0827818 | ||||||||
\(428\) | −6.46021e6 | −1.70466 | ||||||||
\(429\) | 3.62087e6 | 0.949881 | ||||||||
\(430\) | −5.19139e6 | −1.35398 | ||||||||
\(431\) | 2.80235e6 | 0.726658 | 0.363329 | − | 0.931661i | \(-0.381640\pi\) | ||||
0.363329 | + | 0.931661i | \(0.381640\pi\) | |||||||
\(432\) | −2.43778e6 | −0.628470 | ||||||||
\(433\) | 3.06756e6 | 0.786272 | 0.393136 | − | 0.919480i | \(-0.371390\pi\) | ||||
0.393136 | + | 0.919480i | \(0.371390\pi\) | |||||||
\(434\) | 9.25433e6 | 2.35842 | ||||||||
\(435\) | −2.61025e6 | −0.661393 | ||||||||
\(436\) | −2.28900e6 | −0.576672 | ||||||||
\(437\) | −692877. | −0.173561 | ||||||||
\(438\) | −7.82656e6 | −1.94933 | ||||||||
\(439\) | −4.01436e6 | −0.994158 | −0.497079 | − | 0.867705i | \(-0.665594\pi\) | ||||
−0.497079 | + | 0.867705i | \(0.665594\pi\) | |||||||
\(440\) | 2.17575e7 | 5.35769 | ||||||||
\(441\) | −228992. | −0.0560690 | ||||||||
\(442\) | 4.87880e6 | 1.18784 | ||||||||
\(443\) | 4.74625e6 | 1.14906 | 0.574528 | − | 0.818485i | \(-0.305186\pi\) | ||||
0.574528 | + | 0.818485i | \(0.305186\pi\) | |||||||
\(444\) | 7.89767e6 | 1.90126 | ||||||||
\(445\) | 1.17382e6 | 0.280998 | ||||||||
\(446\) | 1.06646e7 | 2.53869 | ||||||||
\(447\) | −1.19223e6 | −0.282222 | ||||||||
\(448\) | −1.03897e7 | −2.44573 | ||||||||
\(449\) | 1.57070e6 | 0.367687 | 0.183843 | − | 0.982956i | \(-0.441146\pi\) | ||||
0.183843 | + | 0.982956i | \(0.441146\pi\) | |||||||
\(450\) | −332204. | −0.0773345 | ||||||||
\(451\) | −3.43393e6 | −0.794968 | ||||||||
\(452\) | −1.01420e7 | −2.33495 | ||||||||
\(453\) | −1.54494e6 | −0.353725 | ||||||||
\(454\) | −287410. | −0.0654429 | ||||||||
\(455\) | 3.36018e6 | 0.760911 | ||||||||
\(456\) | 6.60200e6 | 1.48684 | ||||||||
\(457\) | 4.94573e6 | 1.10775 | 0.553873 | − | 0.832601i | \(-0.313149\pi\) | ||||
0.553873 | + | 0.832601i | \(0.313149\pi\) | |||||||
\(458\) | 1.62186e6 | 0.361284 | ||||||||
\(459\) | 608710. | 0.134859 | ||||||||
\(460\) | 2.32779e6 | 0.512919 | ||||||||
\(461\) | 4.86491e6 | 1.06616 | 0.533080 | − | 0.846065i | \(-0.321035\pi\) | ||||
0.533080 | + | 0.846065i | \(0.321035\pi\) | |||||||
\(462\) | 8.49949e6 | 1.85263 | ||||||||
\(463\) | −2.04379e6 | −0.443082 | −0.221541 | − | 0.975151i | \(-0.571109\pi\) | ||||
−0.221541 | + | 0.975151i | \(0.571109\pi\) | |||||||
\(464\) | 1.85139e7 | 3.99211 | ||||||||
\(465\) | 3.42621e6 | 0.734822 | ||||||||
\(466\) | 1.39391e7 | 2.97351 | ||||||||
\(467\) | −6.33570e6 | −1.34432 | −0.672159 | − | 0.740407i | \(-0.734633\pi\) | ||||
−0.672159 | + | 0.740407i | \(0.734633\pi\) | |||||||
\(468\) | −3.69118e6 | −0.779025 | ||||||||
\(469\) | −2.49107e6 | −0.522942 | ||||||||
\(470\) | 8.61671e6 | 1.79927 | ||||||||
\(471\) | 3.23866e6 | 0.672688 | ||||||||
\(472\) | 3.60472e6 | 0.744760 | ||||||||
\(473\) | −6.82362e6 | −1.40237 | ||||||||
\(474\) | −3.79082e6 | −0.774975 | ||||||||
\(475\) | 498759. | 0.101428 | ||||||||
\(476\) | 8.29306e6 | 1.67763 | ||||||||
\(477\) | −2.93243e6 | −0.590107 | ||||||||
\(478\) | −1.47443e6 | −0.295158 | ||||||||
\(479\) | 2.39044e6 | 0.476036 | 0.238018 | − | 0.971261i | \(-0.423502\pi\) | ||||
0.238018 | + | 0.971261i | \(0.423502\pi\) | |||||||
\(480\) | −8.53079e6 | −1.69000 | ||||||||
\(481\) | 5.66733e6 | 1.11690 | ||||||||
\(482\) | −3.06735e6 | −0.601375 | ||||||||
\(483\) | 562925. | 0.109795 | ||||||||
\(484\) | 3.26690e7 | 6.33902 | ||||||||
\(485\) | −1.55714e6 | −0.300589 | ||||||||
\(486\) | −635977. | −0.122138 | ||||||||
\(487\) | −8.69235e6 | −1.66079 | −0.830395 | − | 0.557175i | \(-0.811885\pi\) | ||||
−0.830395 | + | 0.557175i | \(0.811885\pi\) | |||||||
\(488\) | −1.47735e6 | −0.280824 | ||||||||
\(489\) | −4.09190e6 | −0.773843 | ||||||||
\(490\) | −1.59504e6 | −0.300111 | ||||||||
\(491\) | 3.02753e6 | 0.566742 | 0.283371 | − | 0.959010i | \(-0.408547\pi\) | ||||
0.283371 | + | 0.959010i | \(0.408547\pi\) | |||||||
\(492\) | 3.50062e6 | 0.651976 | ||||||||
\(493\) | −4.62290e6 | −0.856638 | ||||||||
\(494\) | 7.65299e6 | 1.41096 | ||||||||
\(495\) | 3.14675e6 | 0.577230 | ||||||||
\(496\) | −2.43013e7 | −4.43533 | ||||||||
\(497\) | −8.82853e6 | −1.60324 | ||||||||
\(498\) | −9.83526e6 | −1.77710 | ||||||||
\(499\) | 3.24808e6 | 0.583950 | 0.291975 | − | 0.956426i | \(-0.405688\pi\) | ||||
0.291975 | + | 0.956426i | \(0.405688\pi\) | |||||||
\(500\) | −1.54267e7 | −2.75962 | ||||||||
\(501\) | 3.23853e6 | 0.576440 | ||||||||
\(502\) | 1.35866e7 | 2.40631 | ||||||||
\(503\) | −1.14587e6 | −0.201937 | −0.100969 | − | 0.994890i | \(-0.532194\pi\) | ||||
−0.100969 | + | 0.994890i | \(0.532194\pi\) | |||||||
\(504\) | −5.36377e6 | −0.940576 | ||||||||
\(505\) | 5.07401e6 | 0.885367 | ||||||||
\(506\) | 4.22526e6 | 0.733630 | ||||||||
\(507\) | 692859. | 0.119709 | ||||||||
\(508\) | −1.18291e7 | −2.03373 | ||||||||
\(509\) | −7.47756e6 | −1.27928 | −0.639640 | − | 0.768675i | \(-0.720917\pi\) | ||||
−0.639640 | + | 0.768675i | \(0.720917\pi\) | |||||||
\(510\) | 4.23997e6 | 0.721834 | ||||||||
\(511\) | −9.54667e6 | −1.61733 | ||||||||
\(512\) | 576256. | 0.0971494 | ||||||||
\(513\) | 954834. | 0.160190 | ||||||||
\(514\) | 5.95298e6 | 0.993863 | ||||||||
\(515\) | 109019. | 0.0181128 | ||||||||
\(516\) | 6.95613e6 | 1.15012 | ||||||||
\(517\) | 1.13259e7 | 1.86357 | ||||||||
\(518\) | 1.33033e7 | 2.17838 | ||||||||
\(519\) | 2.77223e6 | 0.451763 | ||||||||
\(520\) | −1.59163e7 | −2.58127 | ||||||||
\(521\) | −568216. | −0.0917106 | −0.0458553 | − | 0.998948i | \(-0.514601\pi\) | ||||
−0.0458553 | + | 0.998948i | \(0.514601\pi\) | |||||||
\(522\) | 4.82998e6 | 0.775835 | ||||||||
\(523\) | 6.11824e6 | 0.978076 | 0.489038 | − | 0.872262i | \(-0.337348\pi\) | ||||
0.489038 | + | 0.872262i | \(0.337348\pi\) | |||||||
\(524\) | −1.15102e7 | −1.83128 | ||||||||
\(525\) | −405215. | −0.0641634 | ||||||||
\(526\) | −7.01703e6 | −1.10583 | ||||||||
\(527\) | 6.06801e6 | 0.951743 | ||||||||
\(528\) | −2.23191e7 | −3.48411 | ||||||||
\(529\) | 279841. | 0.0434783 | ||||||||
\(530\) | −2.04258e7 | −3.15856 | ||||||||
\(531\) | 521343. | 0.0802394 | ||||||||
\(532\) | 1.30087e7 | 1.99275 | ||||||||
\(533\) | 2.51203e6 | 0.383007 | ||||||||
\(534\) | −2.17203e6 | −0.329620 | ||||||||
\(535\) | −4.02880e6 | −0.608543 | ||||||||
\(536\) | 1.17995e7 | 1.77400 | ||||||||
\(537\) | −5.66004e6 | −0.847001 | ||||||||
\(538\) | 1.75189e7 | 2.60947 | ||||||||
\(539\) | −2.09654e6 | −0.310836 | ||||||||
\(540\) | −3.20786e6 | −0.473403 | ||||||||
\(541\) | −4.31434e6 | −0.633755 | −0.316878 | − | 0.948466i | \(-0.602634\pi\) | ||||
−0.316878 | + | 0.948466i | \(0.602634\pi\) | |||||||
\(542\) | 5.67110e6 | 0.829219 | ||||||||
\(543\) | 6.00314e6 | 0.873733 | ||||||||
\(544\) | −1.51085e7 | −2.18889 | ||||||||
\(545\) | −1.42749e6 | −0.205865 | ||||||||
\(546\) | −6.21764e6 | −0.892574 | ||||||||
\(547\) | 7.34052e6 | 1.04896 | 0.524480 | − | 0.851423i | \(-0.324260\pi\) | ||||
0.524480 | + | 0.851423i | \(0.324260\pi\) | |||||||
\(548\) | 6.18471e6 | 0.879767 | ||||||||
\(549\) | −213667. | −0.0302556 | ||||||||
\(550\) | −3.04150e6 | −0.428728 | ||||||||
\(551\) | −7.25157e6 | −1.01754 | ||||||||
\(552\) | −2.66643e6 | −0.372463 | ||||||||
\(553\) | −4.62396e6 | −0.642986 | ||||||||
\(554\) | 1.10906e6 | 0.153526 | ||||||||
\(555\) | 4.92525e6 | 0.678728 | ||||||||
\(556\) | 1.79972e7 | 2.46898 | ||||||||
\(557\) | 8.10617e6 | 1.10708 | 0.553538 | − | 0.832824i | \(-0.313277\pi\) | ||||
0.553538 | + | 0.832824i | \(0.313277\pi\) | |||||||
\(558\) | −6.33983e6 | −0.861970 | ||||||||
\(559\) | 4.99169e6 | 0.675644 | ||||||||
\(560\) | −2.07123e7 | −2.79098 | ||||||||
\(561\) | 5.57306e6 | 0.747630 | ||||||||
\(562\) | −1.93013e7 | −2.57779 | ||||||||
\(563\) | 1.15177e7 | 1.53142 | 0.765709 | − | 0.643187i | \(-0.222388\pi\) | ||||
0.765709 | + | 0.643187i | \(0.222388\pi\) | |||||||
\(564\) | −1.15459e7 | −1.52837 | ||||||||
\(565\) | −6.32489e6 | −0.833550 | ||||||||
\(566\) | −1.14774e7 | −1.50592 | ||||||||
\(567\) | −775752. | −0.101336 | ||||||||
\(568\) | 4.18185e7 | 5.43873 | ||||||||
\(569\) | 248635. | 0.0321945 | 0.0160972 | − | 0.999870i | \(-0.494876\pi\) | ||||
0.0160972 | + | 0.999870i | \(0.494876\pi\) | |||||||
\(570\) | 6.65090e6 | 0.857419 | ||||||||
\(571\) | 2.55456e6 | 0.327888 | 0.163944 | − | 0.986470i | \(-0.447578\pi\) | ||||
0.163944 | + | 0.986470i | \(0.447578\pi\) | |||||||
\(572\) | −3.37947e7 | −4.31876 | ||||||||
\(573\) | −5.15994e6 | −0.656536 | ||||||||
\(574\) | 5.89664e6 | 0.747007 | ||||||||
\(575\) | −201440. | −0.0254084 | ||||||||
\(576\) | 7.11763e6 | 0.893880 | ||||||||
\(577\) | 3.96849e6 | 0.496233 | 0.248116 | − | 0.968730i | \(-0.420188\pi\) | ||||
0.248116 | + | 0.968730i | \(0.420188\pi\) | |||||||
\(578\) | −7.78311e6 | −0.969022 | ||||||||
\(579\) | −190785. | −0.0236509 | ||||||||
\(580\) | 2.43624e7 | 3.00711 | ||||||||
\(581\) | −1.19968e7 | −1.47444 | ||||||||
\(582\) | 2.88131e6 | 0.352601 | ||||||||
\(583\) | −2.68479e7 | −3.27144 | ||||||||
\(584\) | 4.52201e7 | 5.48655 | ||||||||
\(585\) | −2.30194e6 | −0.278103 | ||||||||
\(586\) | 2.00175e7 | 2.40806 | ||||||||
\(587\) | 7.38560e6 | 0.884689 | 0.442344 | − | 0.896845i | \(-0.354147\pi\) | ||||
0.442344 | + | 0.896845i | \(0.354147\pi\) | |||||||
\(588\) | 2.13725e6 | 0.254925 | ||||||||
\(589\) | 9.51840e6 | 1.13051 | ||||||||
\(590\) | 3.63142e6 | 0.429483 | ||||||||
\(591\) | 3.07986e6 | 0.362713 | ||||||||
\(592\) | −3.49336e7 | −4.09675 | ||||||||
\(593\) | −1.34366e7 | −1.56910 | −0.784552 | − | 0.620063i | \(-0.787107\pi\) | ||||
−0.784552 | + | 0.620063i | \(0.787107\pi\) | |||||||
\(594\) | −5.82271e6 | −0.677109 | ||||||||
\(595\) | 5.17182e6 | 0.598896 | ||||||||
\(596\) | 1.11275e7 | 1.28316 | ||||||||
\(597\) | 291020. | 0.0334185 | ||||||||
\(598\) | −3.09091e6 | −0.353454 | ||||||||
\(599\) | 1.65576e6 | 0.188552 | 0.0942760 | − | 0.995546i | \(-0.469946\pi\) | ||||
0.0942760 | + | 0.995546i | \(0.469946\pi\) | |||||||
\(600\) | 1.91940e6 | 0.217664 | ||||||||
\(601\) | −8.29015e6 | −0.936216 | −0.468108 | − | 0.883671i | \(-0.655064\pi\) | ||||
−0.468108 | + | 0.883671i | \(0.655064\pi\) | |||||||
\(602\) | 1.17173e7 | 1.31776 | ||||||||
\(603\) | 1.70654e6 | 0.191128 | ||||||||
\(604\) | 1.44194e7 | 1.60826 | ||||||||
\(605\) | 2.03734e7 | 2.26296 | ||||||||
\(606\) | −9.38890e6 | −1.03856 | ||||||||
\(607\) | −1.24477e7 | −1.37125 | −0.685624 | − | 0.727956i | \(-0.740470\pi\) | ||||
−0.685624 | + | 0.727956i | \(0.740470\pi\) | |||||||
\(608\) | −2.36995e7 | −2.60004 | ||||||||
\(609\) | 5.89151e6 | 0.643700 | ||||||||
\(610\) | −1.48830e6 | −0.161944 | ||||||||
\(611\) | −8.28525e6 | −0.897848 | ||||||||
\(612\) | −5.68129e6 | −0.613153 | ||||||||
\(613\) | −9.98753e6 | −1.07351 | −0.536756 | − | 0.843737i | \(-0.680351\pi\) | ||||
−0.536756 | + | 0.843737i | \(0.680351\pi\) | |||||||
\(614\) | −2.30275e7 | −2.46505 | ||||||||
\(615\) | 2.18310e6 | 0.232748 | ||||||||
\(616\) | −4.91081e7 | −5.21437 | ||||||||
\(617\) | −1.14994e7 | −1.21608 | −0.608042 | − | 0.793905i | \(-0.708045\pi\) | ||||
−0.608042 | + | 0.793905i | \(0.708045\pi\) | |||||||
\(618\) | −201728. | −0.0212469 | ||||||||
\(619\) | −5.70831e6 | −0.598799 | −0.299400 | − | 0.954128i | \(-0.596786\pi\) | ||||
−0.299400 | + | 0.954128i | \(0.596786\pi\) | |||||||
\(620\) | −3.19780e7 | −3.34096 | ||||||||
\(621\) | −385641. | −0.0401286 | ||||||||
\(622\) | 1.45922e7 | 1.51232 | ||||||||
\(623\) | −2.64940e6 | −0.273481 | ||||||||
\(624\) | 1.63271e7 | 1.67861 | ||||||||
\(625\) | −8.43064e6 | −0.863297 | ||||||||
\(626\) | −5.64138e6 | −0.575373 | ||||||||
\(627\) | 8.74201e6 | 0.888060 | ||||||||
\(628\) | −3.02275e7 | −3.05847 | ||||||||
\(629\) | 8.72288e6 | 0.879090 | ||||||||
\(630\) | −5.40350e6 | −0.542405 | ||||||||
\(631\) | 6.75550e6 | 0.675436 | 0.337718 | − | 0.941247i | \(-0.390345\pi\) | ||||
0.337718 | + | 0.941247i | \(0.390345\pi\) | |||||||
\(632\) | 2.19025e7 | 2.18123 | ||||||||
\(633\) | 9.30592e6 | 0.923102 | ||||||||
\(634\) | 2.79941e7 | 2.76594 | ||||||||
\(635\) | −7.37703e6 | −0.726018 | ||||||||
\(636\) | 2.73693e7 | 2.68300 | ||||||||
\(637\) | 1.53368e6 | 0.149757 | ||||||||
\(638\) | 4.42211e7 | 4.30108 | ||||||||
\(639\) | 6.04813e6 | 0.585961 | ||||||||
\(640\) | 1.92462e7 | 1.85735 | ||||||||
\(641\) | 355815. | 0.0342042 | 0.0171021 | − | 0.999854i | \(-0.494556\pi\) | ||||
0.0171021 | + | 0.999854i | \(0.494556\pi\) | |||||||
\(642\) | 7.45485e6 | 0.713841 | ||||||||
\(643\) | 1.12269e6 | 0.107086 | 0.0535432 | − | 0.998566i | \(-0.482949\pi\) | ||||
0.0535432 | + | 0.998566i | \(0.482949\pi\) | |||||||
\(644\) | −5.25397e6 | −0.499198 | ||||||||
\(645\) | 4.33807e6 | 0.410580 | ||||||||
\(646\) | 1.17791e7 | 1.11053 | ||||||||
\(647\) | −1.91791e7 | −1.80123 | −0.900613 | − | 0.434621i | \(-0.856882\pi\) | ||||
−0.900613 | + | 0.434621i | \(0.856882\pi\) | |||||||
\(648\) | 3.67453e6 | 0.343768 | ||||||||
\(649\) | 4.77317e6 | 0.444831 | ||||||||
\(650\) | 2.22495e6 | 0.206556 | ||||||||
\(651\) | −7.73319e6 | −0.715165 | ||||||||
\(652\) | 3.81911e7 | 3.51838 | ||||||||
\(653\) | −9.62631e6 | −0.883440 | −0.441720 | − | 0.897153i | \(-0.645632\pi\) | ||||
−0.441720 | + | 0.897153i | \(0.645632\pi\) | |||||||
\(654\) | 2.64142e6 | 0.241487 | ||||||||
\(655\) | −7.17813e6 | −0.653745 | ||||||||
\(656\) | −1.54842e7 | −1.40485 | ||||||||
\(657\) | 6.54010e6 | 0.591114 | ||||||||
\(658\) | −1.94485e7 | −1.75114 | ||||||||
\(659\) | −6.82930e6 | −0.612579 | −0.306290 | − | 0.951938i | \(-0.599088\pi\) | ||||
−0.306290 | + | 0.951938i | \(0.599088\pi\) | |||||||
\(660\) | −2.93696e7 | −2.62445 | ||||||||
\(661\) | 9.20374e6 | 0.819333 | 0.409667 | − | 0.912235i | \(-0.365645\pi\) | ||||
0.409667 | + | 0.912235i | \(0.365645\pi\) | |||||||
\(662\) | −1.10813e7 | −0.982755 | ||||||||
\(663\) | −4.07687e6 | −0.360199 | ||||||||
\(664\) | 5.68260e7 | 5.00180 | ||||||||
\(665\) | 8.11263e6 | 0.711389 | ||||||||
\(666\) | −9.11363e6 | −0.796170 | ||||||||
\(667\) | 2.92878e6 | 0.254902 | ||||||||
\(668\) | −3.02263e7 | −2.62086 | ||||||||
\(669\) | −8.91169e6 | −0.769830 | ||||||||
\(670\) | 1.18869e7 | 1.02302 | ||||||||
\(671\) | −1.95623e6 | −0.167731 | ||||||||
\(672\) | 1.92546e7 | 1.64479 | ||||||||
\(673\) | −9.25649e6 | −0.787787 | −0.393893 | − | 0.919156i | \(-0.628872\pi\) | ||||
−0.393893 | + | 0.919156i | \(0.628872\pi\) | |||||||
\(674\) | 1.22244e7 | 1.03652 | ||||||||
\(675\) | 277599. | 0.0234509 | ||||||||
\(676\) | −6.46669e6 | −0.544271 | ||||||||
\(677\) | −4.89629e6 | −0.410578 | −0.205289 | − | 0.978701i | \(-0.565813\pi\) | ||||
−0.205289 | + | 0.978701i | \(0.565813\pi\) | |||||||
\(678\) | 1.17035e7 | 0.977782 | ||||||||
\(679\) | 3.51457e6 | 0.292548 | ||||||||
\(680\) | −2.44976e7 | −2.03166 | ||||||||
\(681\) | 240168. | 0.0198448 | ||||||||
\(682\) | −5.80445e7 | −4.77859 | ||||||||
\(683\) | −1.01443e6 | −0.0832086 | −0.0416043 | − | 0.999134i | \(-0.513247\pi\) | ||||
−0.0416043 | + | 0.999134i | \(0.513247\pi\) | |||||||
\(684\) | −8.91179e6 | −0.728324 | ||||||||
\(685\) | 3.85699e6 | 0.314067 | ||||||||
\(686\) | 2.50030e7 | 2.02853 | ||||||||
\(687\) | −1.35527e6 | −0.109555 | ||||||||
\(688\) | −3.07689e7 | −2.47823 | ||||||||
\(689\) | 1.96401e7 | 1.57614 | ||||||||
\(690\) | −2.68618e6 | −0.214789 | ||||||||
\(691\) | −9.64799e6 | −0.768673 | −0.384336 | − | 0.923193i | \(-0.625570\pi\) | ||||
−0.384336 | + | 0.923193i | \(0.625570\pi\) | |||||||
\(692\) | −2.58741e7 | −2.05400 | ||||||||
\(693\) | −7.10242e6 | −0.561789 | ||||||||
\(694\) | 1.17113e7 | 0.923007 | ||||||||
\(695\) | 1.12236e7 | 0.881396 | ||||||||
\(696\) | −2.79066e7 | −2.18365 | ||||||||
\(697\) | 3.86639e6 | 0.301456 | ||||||||
\(698\) | 1.58585e6 | 0.123204 | ||||||||
\(699\) | −1.16479e7 | −0.901684 | ||||||||
\(700\) | 3.78201e6 | 0.291728 | ||||||||
\(701\) | −1.47825e7 | −1.13620 | −0.568098 | − | 0.822961i | \(-0.692321\pi\) | ||||
−0.568098 | + | 0.822961i | \(0.692321\pi\) | |||||||
\(702\) | 4.25949e6 | 0.326224 | ||||||||
\(703\) | 1.36829e7 | 1.04421 | ||||||||
\(704\) | 6.51657e7 | 4.95550 | ||||||||
\(705\) | −7.20037e6 | −0.545610 | ||||||||
\(706\) | 1.70865e7 | 1.29016 | ||||||||
\(707\) | −1.14524e7 | −0.861683 | ||||||||
\(708\) | −4.86587e6 | −0.364819 | ||||||||
\(709\) | −585189. | −0.0437201 | −0.0218600 | − | 0.999761i | \(-0.506959\pi\) | ||||
−0.0218600 | + | 0.999761i | \(0.506959\pi\) | |||||||
\(710\) | 4.21282e7 | 3.13637 | ||||||||
\(711\) | 3.16772e6 | 0.235003 | ||||||||
\(712\) | 1.25495e7 | 0.927742 | ||||||||
\(713\) | −3.84432e6 | −0.283201 | ||||||||
\(714\) | −9.56989e6 | −0.702524 | ||||||||
\(715\) | −2.10755e7 | −1.54175 | ||||||||
\(716\) | 5.28271e7 | 3.85100 | ||||||||
\(717\) | 1.23208e6 | 0.0895035 | ||||||||
\(718\) | −1.99940e7 | −1.44740 | ||||||||
\(719\) | −3.42448e6 | −0.247043 | −0.123521 | − | 0.992342i | \(-0.539419\pi\) | ||||
−0.123521 | + | 0.992342i | \(0.539419\pi\) | |||||||
\(720\) | 1.41893e7 | 1.02007 | ||||||||
\(721\) | −246064. | −0.0176283 | ||||||||
\(722\) | −8.19147e6 | −0.584816 | ||||||||
\(723\) | 2.56317e6 | 0.182361 | ||||||||
\(724\) | −5.60293e7 | −3.97254 | ||||||||
\(725\) | −2.10825e6 | −0.148963 | ||||||||
\(726\) | −3.76988e7 | −2.65452 | ||||||||
\(727\) | −1.91984e7 | −1.34719 | −0.673595 | − | 0.739100i | \(-0.735251\pi\) | ||||
−0.673595 | + | 0.739100i | \(0.735251\pi\) | |||||||
\(728\) | 3.59242e7 | 2.51222 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 4.55551e7 | 3.16395 | ||||||||
\(731\) | 7.68297e6 | 0.531784 | ||||||||
\(732\) | 1.99422e6 | 0.137561 | ||||||||
\(733\) | 2.66362e7 | 1.83110 | 0.915552 | − | 0.402200i | \(-0.131754\pi\) | ||||
0.915552 | + | 0.402200i | \(0.131754\pi\) | |||||||
\(734\) | −2.17060e7 | −1.48710 | ||||||||
\(735\) | 1.33286e6 | 0.0910053 | ||||||||
\(736\) | 9.57181e6 | 0.651327 | ||||||||
\(737\) | 1.56243e7 | 1.05958 | ||||||||
\(738\) | −4.03959e6 | −0.273021 | ||||||||
\(739\) | −6.81746e6 | −0.459210 | −0.229605 | − | 0.973284i | \(-0.573743\pi\) | ||||
−0.229605 | + | 0.973284i | \(0.573743\pi\) | |||||||
\(740\) | −4.59690e7 | −3.08593 | ||||||||
\(741\) | −6.39506e6 | −0.427857 | ||||||||
\(742\) | 4.61024e7 | 3.07407 | ||||||||
\(743\) | −377932. | −0.0251155 | −0.0125577 | − | 0.999921i | \(-0.503997\pi\) | ||||
−0.0125577 | + | 0.999921i | \(0.503997\pi\) | |||||||
\(744\) | 3.66301e7 | 2.42608 | ||||||||
\(745\) | 6.93946e6 | 0.458073 | ||||||||
\(746\) | −1.43812e7 | −0.946122 | ||||||||
\(747\) | 8.21863e6 | 0.538887 | ||||||||
\(748\) | −5.20152e7 | −3.39920 | ||||||||
\(749\) | 9.09327e6 | 0.592264 | ||||||||
\(750\) | 1.78019e7 | 1.15561 | ||||||||
\(751\) | −8.02610e6 | −0.519283 | −0.259642 | − | 0.965705i | \(-0.583604\pi\) | ||||
−0.259642 | + | 0.965705i | \(0.583604\pi\) | |||||||
\(752\) | 5.10705e7 | 3.29326 | ||||||||
\(753\) | −1.13533e7 | −0.729686 | ||||||||
\(754\) | −3.23491e7 | −2.07221 | ||||||||
\(755\) | 8.99242e6 | 0.574129 | ||||||||
\(756\) | 7.24035e6 | 0.460739 | ||||||||
\(757\) | −4.55894e6 | −0.289150 | −0.144575 | − | 0.989494i | \(-0.546182\pi\) | ||||
−0.144575 | + | 0.989494i | \(0.546182\pi\) | |||||||
\(758\) | −3.06209e7 | −1.93573 | ||||||||
\(759\) | −3.53075e6 | −0.222465 | ||||||||
\(760\) | −3.84274e7 | −2.41328 | ||||||||
\(761\) | 2.77860e7 | 1.73926 | 0.869629 | − | 0.493705i | \(-0.164358\pi\) | ||||
0.869629 | + | 0.493705i | \(0.164358\pi\) | |||||||
\(762\) | 1.36504e7 | 0.851643 | ||||||||
\(763\) | 3.22195e6 | 0.200358 | ||||||||
\(764\) | 4.81595e7 | 2.98503 | ||||||||
\(765\) | −3.54304e6 | −0.218888 | ||||||||
\(766\) | 3.54862e7 | 2.18518 | ||||||||
\(767\) | −3.49173e6 | −0.214315 | ||||||||
\(768\) | −1.03058e7 | −0.630490 | ||||||||
\(769\) | 1.47056e7 | 0.896742 | 0.448371 | − | 0.893847i | \(-0.352004\pi\) | ||||
0.448371 | + | 0.893847i | \(0.352004\pi\) | |||||||
\(770\) | −4.94719e7 | −3.00699 | ||||||||
\(771\) | −4.97448e6 | −0.301378 | ||||||||
\(772\) | 1.78066e6 | 0.107532 | ||||||||
\(773\) | 1.46941e7 | 0.884495 | 0.442248 | − | 0.896893i | \(-0.354181\pi\) | ||||
0.442248 | + | 0.896893i | \(0.354181\pi\) | |||||||
\(774\) | −8.02713e6 | −0.481624 | ||||||||
\(775\) | 2.76729e6 | 0.165501 | ||||||||
\(776\) | −1.66476e7 | −0.992424 | ||||||||
\(777\) | −1.11166e7 | −0.660572 | ||||||||
\(778\) | −5.29919e7 | −3.13878 | ||||||||
\(779\) | 6.06489e6 | 0.358080 | ||||||||
\(780\) | 2.14848e7 | 1.26443 | ||||||||
\(781\) | 5.53738e7 | 3.24845 | ||||||||
\(782\) | −4.75738e6 | −0.278196 | ||||||||
\(783\) | −4.03607e6 | −0.235264 | ||||||||
\(784\) | −9.45368e6 | −0.549301 | ||||||||
\(785\) | −1.88509e7 | −1.09184 | ||||||||
\(786\) | 1.32823e7 | 0.766864 | ||||||||
\(787\) | 1.02770e7 | 0.591465 | 0.295732 | − | 0.955271i | \(-0.404436\pi\) | ||||
0.295732 | + | 0.955271i | \(0.404436\pi\) | |||||||
\(788\) | −2.87454e7 | −1.64912 | ||||||||
\(789\) | 5.86363e6 | 0.335331 | ||||||||
\(790\) | 2.20648e7 | 1.25786 | ||||||||
\(791\) | 1.42757e7 | 0.811253 | ||||||||
\(792\) | 3.36423e7 | 1.90578 | ||||||||
\(793\) | 1.43105e6 | 0.0808110 | ||||||||
\(794\) | −4.45046e7 | −2.50527 | ||||||||
\(795\) | 1.70684e7 | 0.957800 | ||||||||
\(796\) | −2.71618e6 | −0.151942 | ||||||||
\(797\) | 2.13182e7 | 1.18879 | 0.594395 | − | 0.804173i | \(-0.297392\pi\) | ||||
0.594395 | + | 0.804173i | \(0.297392\pi\) | |||||||
\(798\) | −1.50115e7 | −0.834483 | ||||||||
\(799\) | −1.27523e7 | −0.706675 | ||||||||
\(800\) | −6.89015e6 | −0.380631 | ||||||||
\(801\) | 1.81501e6 | 0.0999536 | ||||||||
\(802\) | −3.31641e7 | −1.82068 | ||||||||
\(803\) | 5.98781e7 | 3.27702 | ||||||||
\(804\) | −1.59278e7 | −0.868989 | ||||||||
\(805\) | −3.27655e6 | −0.178208 | ||||||||
\(806\) | 4.24614e7 | 2.30227 | ||||||||
\(807\) | −1.46393e7 | −0.791293 | ||||||||
\(808\) | 5.42470e7 | 2.92312 | ||||||||
\(809\) | 2.64965e7 | 1.42337 | 0.711685 | − | 0.702499i | \(-0.247932\pi\) | ||||
0.711685 | + | 0.702499i | \(0.247932\pi\) | |||||||
\(810\) | 3.70175e6 | 0.198242 | ||||||||
\(811\) | 1.59727e7 | 0.852758 | 0.426379 | − | 0.904545i | \(-0.359789\pi\) | ||||
0.426379 | + | 0.904545i | \(0.359789\pi\) | |||||||
\(812\) | −5.49875e7 | −2.92667 | ||||||||
\(813\) | −4.73893e6 | −0.251452 | ||||||||
\(814\) | −8.34401e7 | −4.41381 | ||||||||
\(815\) | 2.38172e7 | 1.25602 | ||||||||
\(816\) | 2.51299e7 | 1.32119 | ||||||||
\(817\) | 1.20517e7 | 0.631672 | ||||||||
\(818\) | −5.20725e6 | −0.272098 | ||||||||
\(819\) | 5.19564e6 | 0.270663 | ||||||||
\(820\) | −2.03756e7 | −1.05822 | ||||||||
\(821\) | 2.19797e7 | 1.13806 | 0.569029 | − | 0.822317i | \(-0.307319\pi\) | ||||
0.569029 | + | 0.822317i | \(0.307319\pi\) | |||||||
\(822\) | −7.13693e6 | −0.368410 | ||||||||
\(823\) | −3.47354e7 | −1.78761 | −0.893806 | − | 0.448454i | \(-0.851975\pi\) | ||||
−0.893806 | + | 0.448454i | \(0.851975\pi\) | |||||||
\(824\) | 1.16554e6 | 0.0598012 | ||||||||
\(825\) | 2.54157e6 | 0.130007 | ||||||||
\(826\) | −8.19635e6 | −0.417994 | ||||||||
\(827\) | −1.25679e7 | −0.638997 | −0.319499 | − | 0.947587i | \(-0.603515\pi\) | ||||
−0.319499 | + | 0.947587i | \(0.603515\pi\) | |||||||
\(828\) | 3.59932e6 | 0.182450 | ||||||||
\(829\) | −3.35386e7 | −1.69495 | −0.847477 | − | 0.530831i | \(-0.821880\pi\) | ||||
−0.847477 | + | 0.530831i | \(0.821880\pi\) | |||||||
\(830\) | 5.72469e7 | 2.88441 | ||||||||
\(831\) | −926766. | −0.0465551 | ||||||||
\(832\) | −4.76708e7 | −2.38750 | ||||||||
\(833\) | 2.36057e6 | 0.117870 | ||||||||
\(834\) | −2.07681e7 | −1.03391 | ||||||||
\(835\) | −1.88501e7 | −0.935617 | ||||||||
\(836\) | −8.15921e7 | −4.03769 | ||||||||
\(837\) | 5.29774e6 | 0.261383 | ||||||||
\(838\) | 1.63442e7 | 0.803996 | ||||||||
\(839\) | 1.15158e6 | 0.0564791 | 0.0282395 | − | 0.999601i | \(-0.491010\pi\) | ||||
0.0282395 | + | 0.999601i | \(0.491010\pi\) | |||||||
\(840\) | 3.12202e7 | 1.52664 | ||||||||
\(841\) | 1.01412e7 | 0.494422 | ||||||||
\(842\) | 4.05240e7 | 1.96984 | ||||||||
\(843\) | 1.61288e7 | 0.781686 | ||||||||
\(844\) | −8.68552e7 | −4.19701 | ||||||||
\(845\) | −4.03284e6 | −0.194298 | ||||||||
\(846\) | 1.33235e7 | 0.640018 | ||||||||
\(847\) | −4.59842e7 | −2.20242 | ||||||||
\(848\) | −1.21062e8 | −5.78121 | ||||||||
\(849\) | 9.59081e6 | 0.456653 | ||||||||
\(850\) | 3.42454e6 | 0.162576 | ||||||||
\(851\) | −5.52628e6 | −0.261583 | ||||||||
\(852\) | −5.64492e7 | −2.66415 | ||||||||
\(853\) | −1.19102e7 | −0.560465 | −0.280232 | − | 0.959932i | \(-0.590411\pi\) | ||||
−0.280232 | + | 0.959932i | \(0.590411\pi\) | |||||||
\(854\) | 3.35918e6 | 0.157612 | ||||||||
\(855\) | −5.55768e6 | −0.260003 | ||||||||
\(856\) | −4.30725e7 | −2.00916 | ||||||||
\(857\) | −1.59627e7 | −0.742430 | −0.371215 | − | 0.928547i | \(-0.621059\pi\) | ||||
−0.371215 | + | 0.928547i | \(0.621059\pi\) | |||||||
\(858\) | 3.89979e7 | 1.80852 | ||||||||
\(859\) | 1.22935e7 | 0.568452 | 0.284226 | − | 0.958757i | \(-0.408263\pi\) | ||||
0.284226 | + | 0.958757i | \(0.408263\pi\) | |||||||
\(860\) | −4.04887e7 | −1.86676 | ||||||||
\(861\) | −4.92740e6 | −0.226522 | ||||||||
\(862\) | 3.01823e7 | 1.38351 | ||||||||
\(863\) | −2.14243e7 | −0.979219 | −0.489609 | − | 0.871942i | \(-0.662861\pi\) | ||||
−0.489609 | + | 0.871942i | \(0.662861\pi\) | |||||||
\(864\) | −1.31906e7 | −0.601148 | ||||||||
\(865\) | −1.61360e7 | −0.733254 | ||||||||
\(866\) | 3.30386e7 | 1.49702 | ||||||||
\(867\) | 6.50380e6 | 0.293846 | ||||||||
\(868\) | 7.21764e7 | 3.25159 | ||||||||
\(869\) | 2.90022e7 | 1.30281 | ||||||||
\(870\) | −2.81133e7 | −1.25925 | ||||||||
\(871\) | −1.14297e7 | −0.510492 | ||||||||
\(872\) | −1.52615e7 | −0.679684 | ||||||||
\(873\) | −2.40771e6 | −0.106922 | ||||||||
\(874\) | −7.46251e6 | −0.330451 | ||||||||
\(875\) | 2.17144e7 | 0.958799 | ||||||||
\(876\) | −6.10409e7 | −2.68758 | ||||||||
\(877\) | −3.70233e6 | −0.162546 | −0.0812730 | − | 0.996692i | \(-0.525899\pi\) | ||||
−0.0812730 | + | 0.996692i | \(0.525899\pi\) | |||||||
\(878\) | −4.32360e7 | −1.89282 | ||||||||
\(879\) | −1.67272e7 | −0.730217 | ||||||||
\(880\) | 1.29910e8 | 5.65505 | ||||||||
\(881\) | 5.90856e6 | 0.256473 | 0.128237 | − | 0.991744i | \(-0.459068\pi\) | ||||
0.128237 | + | 0.991744i | \(0.459068\pi\) | |||||||
\(882\) | −2.46631e6 | −0.106752 | ||||||||
\(883\) | 1.83087e7 | 0.790233 | 0.395117 | − | 0.918631i | \(-0.370704\pi\) | ||||
0.395117 | + | 0.918631i | \(0.370704\pi\) | |||||||
\(884\) | 3.80508e7 | 1.63769 | ||||||||
\(885\) | −3.03452e6 | −0.130236 | ||||||||
\(886\) | 5.11186e7 | 2.18774 | ||||||||
\(887\) | 2.01751e7 | 0.861005 | 0.430503 | − | 0.902589i | \(-0.358336\pi\) | ||||
0.430503 | + | 0.902589i | \(0.358336\pi\) | |||||||
\(888\) | 5.26565e7 | 2.24089 | ||||||||
\(889\) | 1.66505e7 | 0.706597 | ||||||||
\(890\) | 1.26425e7 | 0.535004 | ||||||||
\(891\) | 4.86562e6 | 0.205326 | ||||||||
\(892\) | 8.31757e7 | 3.50013 | ||||||||
\(893\) | −2.00034e7 | −0.839413 | ||||||||
\(894\) | −1.28407e7 | −0.537335 | ||||||||
\(895\) | 3.29447e7 | 1.37476 | ||||||||
\(896\) | −4.34399e7 | −1.80767 | ||||||||
\(897\) | 2.58285e6 | 0.107181 | ||||||||
\(898\) | 1.69170e7 | 0.700055 | ||||||||
\(899\) | −4.02342e7 | −1.66034 | ||||||||
\(900\) | −2.59093e6 | −0.106622 | ||||||||
\(901\) | 3.02291e7 | 1.24055 | ||||||||
\(902\) | −3.69845e7 | −1.51357 | ||||||||
\(903\) | −9.79132e6 | −0.399597 | ||||||||
\(904\) | −6.76203e7 | −2.75205 | ||||||||
\(905\) | −3.49417e7 | −1.41815 | ||||||||
\(906\) | −1.66395e7 | −0.673471 | ||||||||
\(907\) | −3.53066e7 | −1.42508 | −0.712538 | − | 0.701634i | \(-0.752454\pi\) | ||||
−0.712538 | + | 0.701634i | \(0.752454\pi\) | |||||||
\(908\) | −2.24157e6 | −0.0902272 | ||||||||
\(909\) | 7.84564e6 | 0.314933 | ||||||||
\(910\) | 3.61902e7 | 1.44873 | ||||||||
\(911\) | −1.91557e7 | −0.764720 | −0.382360 | − | 0.924014i | \(-0.624889\pi\) | ||||
−0.382360 | + | 0.924014i | \(0.624889\pi\) | |||||||
\(912\) | 3.94193e7 | 1.56936 | ||||||||
\(913\) | 7.52459e7 | 2.98749 | ||||||||
\(914\) | 5.32672e7 | 2.10909 | ||||||||
\(915\) | 1.24366e6 | 0.0491077 | ||||||||
\(916\) | 1.26492e7 | 0.498108 | ||||||||
\(917\) | 1.62015e7 | 0.636257 | ||||||||
\(918\) | 6.55601e6 | 0.256763 | ||||||||
\(919\) | −3.36053e7 | −1.31256 | −0.656279 | − | 0.754518i | \(-0.727871\pi\) | ||||
−0.656279 | + | 0.754518i | \(0.727871\pi\) | |||||||
\(920\) | 1.55202e7 | 0.604542 | ||||||||
\(921\) | 1.92425e7 | 0.747501 | ||||||||
\(922\) | 5.23966e7 | 2.02991 | ||||||||
\(923\) | −4.05077e7 | −1.56507 | ||||||||
\(924\) | 6.62892e7 | 2.55425 | ||||||||
\(925\) | 3.97803e6 | 0.152867 | ||||||||
\(926\) | −2.20123e7 | −0.843602 | ||||||||
\(927\) | 168570. | 0.00644289 | ||||||||
\(928\) | 1.00177e8 | 3.81856 | ||||||||
\(929\) | −2.51698e7 | −0.956842 | −0.478421 | − | 0.878131i | \(-0.658791\pi\) | ||||
−0.478421 | + | 0.878131i | \(0.658791\pi\) | |||||||
\(930\) | 3.69014e7 | 1.39906 | ||||||||
\(931\) | 3.70284e6 | 0.140011 | ||||||||
\(932\) | 1.08714e8 | 4.09963 | ||||||||
\(933\) | −1.21937e7 | −0.458596 | ||||||||
\(934\) | −6.82375e7 | −2.55951 | ||||||||
\(935\) | −3.24384e7 | −1.21347 | ||||||||
\(936\) | −2.46104e7 | −0.918183 | ||||||||
\(937\) | −2.32062e7 | −0.863484 | −0.431742 | − | 0.901997i | \(-0.642101\pi\) | ||||
−0.431742 | + | 0.901997i | \(0.642101\pi\) | |||||||
\(938\) | −2.68296e7 | −0.995651 | ||||||||
\(939\) | 4.71410e6 | 0.174476 | ||||||||
\(940\) | 6.72035e7 | 2.48069 | ||||||||
\(941\) | −1.44758e7 | −0.532930 | −0.266465 | − | 0.963845i | \(-0.585856\pi\) | ||||
−0.266465 | + | 0.963845i | \(0.585856\pi\) | |||||||
\(942\) | 3.48815e7 | 1.28076 | ||||||||
\(943\) | −2.44951e6 | −0.0897014 | ||||||||
\(944\) | 2.15231e7 | 0.786095 | ||||||||
\(945\) | 4.51532e6 | 0.164478 | ||||||||
\(946\) | −7.34926e7 | −2.67003 | ||||||||
\(947\) | −3.57094e7 | −1.29392 | −0.646960 | − | 0.762524i | \(-0.723960\pi\) | ||||
−0.646960 | + | 0.762524i | \(0.723960\pi\) | |||||||
\(948\) | −2.95654e7 | −1.06847 | ||||||||
\(949\) | −4.38027e7 | −1.57883 | ||||||||
\(950\) | 5.37180e6 | 0.193113 | ||||||||
\(951\) | −2.33926e7 | −0.838741 | ||||||||
\(952\) | 5.52927e7 | 1.97731 | ||||||||
\(953\) | −6.09472e6 | −0.217381 | −0.108691 | − | 0.994076i | \(-0.534666\pi\) | ||||
−0.108691 | + | 0.994076i | \(0.534666\pi\) | |||||||
\(954\) | −3.15832e7 | −1.12353 | ||||||||
\(955\) | 3.00338e7 | 1.06562 | ||||||||
\(956\) | −1.14994e7 | −0.406940 | ||||||||
\(957\) | −3.69524e7 | −1.30426 | ||||||||
\(958\) | 2.57459e7 | 0.906345 | ||||||||
\(959\) | −8.70548e6 | −0.305665 | ||||||||
\(960\) | −4.14287e7 | −1.45085 | ||||||||
\(961\) | 2.41822e7 | 0.844669 | ||||||||
\(962\) | 6.10391e7 | 2.12652 | ||||||||
\(963\) | −6.22949e6 | −0.216464 | ||||||||
\(964\) | −2.39229e7 | −0.829127 | ||||||||
\(965\) | 1.11048e6 | 0.0383877 | ||||||||
\(966\) | 6.06289e6 | 0.209044 | ||||||||
\(967\) | 1.48405e7 | 0.510366 | 0.255183 | − | 0.966893i | \(-0.417864\pi\) | ||||
0.255183 | + | 0.966893i | \(0.417864\pi\) | |||||||
\(968\) | 2.17815e8 | 7.47137 | ||||||||
\(969\) | −9.84296e6 | −0.336757 | ||||||||
\(970\) | −1.67709e7 | −0.572304 | ||||||||
\(971\) | 1.73779e7 | 0.591493 | 0.295746 | − | 0.955267i | \(-0.404432\pi\) | ||||
0.295746 | + | 0.955267i | \(0.404432\pi\) | |||||||
\(972\) | −4.96012e6 | −0.168394 | ||||||||
\(973\) | −2.53325e7 | −0.857818 | ||||||||
\(974\) | −9.36194e7 | −3.16205 | ||||||||
\(975\) | −1.85924e6 | −0.0626359 | ||||||||
\(976\) | −8.82100e6 | −0.296410 | ||||||||
\(977\) | −1.30124e7 | −0.436136 | −0.218068 | − | 0.975934i | \(-0.569976\pi\) | ||||
−0.218068 | + | 0.975934i | \(0.569976\pi\) | |||||||
\(978\) | −4.40711e7 | −1.47335 | ||||||||
\(979\) | 1.66174e7 | 0.554123 | ||||||||
\(980\) | −1.24400e7 | −0.413768 | ||||||||
\(981\) | −2.20725e6 | −0.0732282 | ||||||||
\(982\) | 3.26075e7 | 1.07904 | ||||||||
\(983\) | 1.94435e7 | 0.641787 | 0.320893 | − | 0.947115i | \(-0.396017\pi\) | ||||
0.320893 | + | 0.947115i | \(0.396017\pi\) | |||||||
\(984\) | 2.33398e7 | 0.768440 | ||||||||
\(985\) | −1.79266e7 | −0.588717 | ||||||||
\(986\) | −4.97902e7 | −1.63099 | ||||||||
\(987\) | 1.62517e7 | 0.531015 | ||||||||
\(988\) | 5.96872e7 | 1.94531 | ||||||||
\(989\) | −4.86745e6 | −0.158238 | ||||||||
\(990\) | 3.38915e7 | 1.09901 | ||||||||
\(991\) | −3.56706e6 | −0.115379 | −0.0576894 | − | 0.998335i | \(-0.518373\pi\) | ||||
−0.0576894 | + | 0.998335i | \(0.518373\pi\) | |||||||
\(992\) | −1.31493e8 | −4.24251 | ||||||||
\(993\) | 9.25984e6 | 0.298010 | ||||||||
\(994\) | −9.50862e7 | −3.05247 | ||||||||
\(995\) | −1.69390e6 | −0.0542414 | ||||||||
\(996\) | −7.67072e7 | −2.45012 | ||||||||
\(997\) | 3.36336e7 | 1.07161 | 0.535804 | − | 0.844342i | \(-0.320009\pi\) | ||||
0.535804 | + | 0.844342i | \(0.320009\pi\) | |||||||
\(998\) | 3.49829e7 | 1.11181 | ||||||||
\(999\) | 7.61561e6 | 0.241430 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 69.6.a.a.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 207.6.a.a.1.1 | 2 | |||
4.3 | odd | 2 | 1104.6.a.h.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
69.6.a.a.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
207.6.a.a.1.1 | 2 | 3.2 | odd | 2 | |||
1104.6.a.h.1.2 | 2 | 4.3 | odd | 2 |